Question

Which of these equations has infinitely many solutions? 3(1-2x + 1) = -6x + 2. 4 + 2(x - 5) = 1/2 {(4x - 12) (5x + 15) 3x - 5 = 5= 1/(5x () which statement explains a way you can tell the equation has infinitely many solutions? It is equivalent to an equation that has the same variable terms but different constant terms on either side of the equal sign. It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign. It is equivalent to an equation that has different variable terms on either side of the equation.

Answer 1

The equation with infinite solutions is Option B

4 + 2 (x - 5) = ½ (4x - 12)

The key way to know if an equation has infinite solutions is shown in Option B

It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.

Step-by-step explanation

The key way to know if an equation has infinite solutions is when

It is equivalent to an equation that has the same variable terms and the same constant terms on either side of the equal sign.

So, we will check each of the equations to know which one satisfies that condition.

2x + 1 = -6x + 2

2x + 6x = 2 - 1

8x = 1

Divide both sides by 8

(8x/8) = (1/8)

x = (1/8)

This is not the equation with infinite solutions.

4 + 2 (x - 5) = ½ (4x - 12)

4 + 2x - 10 = 2x - 6

2x - 6 = 2x - 6

2x - 2x = 6 - 6

0 = 0

This is the equation with infinite solutions.

3x - 5 = (1/5) (5x + 15)

3x - 5 = x + 3

3x - x = 3 + 5

2x = 8

Divide both sides by 2

(2x/2) = (8/2)

x = 4

This is not the equation with infinite solutions.

Hope this Helps!!!